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1. I tried going back to the older 2.3 wordpress version. But still the error did not go.. So came back to 2.3.1.
2. Added ini_set("memory_limit","20M"); to the plugin php file from which the error was coming.
   But still the error did not go.
3. Commented the following line in cache.php.
   $data = unserialize(serialize($data));
   The above line was commented at all the 3 places in cache.php.
   But still the error did not go.
4. In php.ini, increased the memory limit from 8M to 20M :
   memory_limit = 20M ; Maximum amount of memory a script may consume (8MB)
   But still the error did not go.
5. In .htaccess, added the following line and restarted the server.
   php_value memory_limit 32M
   But still the error did not go.
6. Deactivated all plugins by moving them from the plugins folder and also by running the following query in phpMyadmin :
   

   update wp_options set option_value  = '' where option_name = 'active_plugins'

   The error was gone, but i can't work well without the plugins. So, only deactivated the plugin with the error and reactivated the rest. The error was gone.
7. But since i wanted that plugin also, i experimented further and added the line ini_set("memory_limit","12M"); to the main root file of the plugin.The plugin had lots of files in subfolders and the error file was inside the folder.
   Adding the line in the root php file which was the starting point of the plugin solved the problem.

Now, everything is working fine.
Just see if one of the above solutions work for you.
Also, check whether you have latest versions of all plugins & themes or try moving some themes or plugins temporarily to check whether that is the cause of problem